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Partition Inequalities and the Network Design Problem with Connectivity Requirements

by

Hervé KerivinUniversity of Minnesota

Monday, April 28, 20033:30 pm

402 Walter Library

The network design problem with connectivity requirements models a wide variety of celebrated combinatorial optimization problems including the minimum spanning tree, Steiner tree, and survivable network design problems. It has applications to the design of reliable communication and transportation networks. Informally given requirements for the number of edge-disjoint paths between every pair of nodes, it consists in designing a minimum cost network that satisfies these requirements.
A way to formulate this problem is to use the well-known cuxtset model which is based on the so called cut inequalities. This formulation is known to be weak and the objective value of the linear programming relaxation is typically significantly less than the objective value of the integer program. Strong formulations are very useful in developing exact algorithm solution methods (i.e., branch-and-cut) since their use rapidly accelerates these solution techniques.
Partition inequalities generally cut inequalities and arise as valid inequalities or facets for optimization problems related to the network design problem with connectivity requirements. These inequalities have received special attention over the past twenty years as people investigated the polyhedral structure of the problem. This talk will give an overview of research on the partition inequalities, with a particular emphasis on their associated separation problem.

Dr. Hervé Kerivin is a joint postdoctoral associate at the Institute for Mathematics and its Applications (IMA) and the Digital Technology Center (DTC) at the University of Minnesota, since September 2002. He received his Ph.D. in Integer and Combinatorial Optimization from the University Blaise Pascal, Clermont-Ferrand, France in November 2000. Dr. Kerivin then moved on to France Telecom Research and Development (December 2000 – August 2002) in Paris, France, where he was a research staff member of the Optimization, Architectures and Traffic Laboratory.
He has worked on some important optimization problems solved during a transportation and communication network planning process. This involves topology computation, traffic prediction and modeling, facility location, determination of the routing strategy, dimensioning, etc. In its more general sense, his research activities seek to investigate these problems using polyhedral combinatorics, in order to develop efficient algorithms, but also to make fundamental contributions to integer and combinatorial optimization.